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The phrase "a set of nine" is correct and usable in written English.
It can be used when referring to a collection or group that contains nine items or elements.
Example: "The artist presented a set of nine paintings that explore the theme of nature."
Alternatives: "a group of nine" or "a collection of nine".
Exact(60)
Dubois Collection's Corksters; $75 for a set of nine.
The representation of the kinetics involved required the evaluation of a set of nine parameters.
The centerpiece of our new architecture is a set of nine relatively independent business divisions.
A set of nine pairs of socks, eight cellphones, nine 45-r.p.m. records.
So far, its most useful feature is a set of nine "Letters to Bad Bosses".
The dynamic responses of the injector are then obtained by solving a set of nine equations simultaneously.
Here, we describe the design of a set of nine novel camphane-based derivatives following these requirements.
Serious aficionados might opt for "Waspwaist," a nine-thousand-dollar aluminum sculpture, from a set of nine.
The result is a set of nine, first-order, fully-coupled, hyperbolic partial differential equations with velocities and stress components as the unknowns.
Application of the model to a set of nine test specimens from aluminum alloy loaded by three different loading regimes is shown.
As for the experimental campaign, reference is made to a set of nine experiments performed using water as working fluid and providing a thermal power of 2 kW.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com